In the debate, real estate magnate Donald Trump told a story linking vaccination to autism. Sen. Rand Paul, a Kentucky Republican and ophthalmologist, suggested that it would be safer to spread out recommended vaccines, rather than give babies and toddlers several vaccines at one visit, a practice that aims to prevent children from missing key shots.

Multiple studies have found no link between vaccines and autism, Karen Remley, executive director of the American Academy of Pediatrics​, said.

"Claims that vaccines are linked to autism, or are unsafe when administered according to the recommended schedule, have been disproven by a robust body of medical literature," Remley said. "It is dangerous to public health to suggest otherwise."

Arthur Caplan, the director of medical ethics at NYU Langone Medical Center in New York, said public health is too serious an issue to become a political football.

"No one should tolerate outright lying that puts vulnerable kids at risk from a would-be President,' Caplan wrote in a blog on bioethics.net. "So Donald, show us your proof, or leave Americas kids alone."

Both critics and supporters of vaccines took to social media Wednesday night to comment.

Health experts are concerned about a resurgence of vaccine-preventable diseases, including measles.

Research shows that the measles outbreak that began at Disneyland last year – which sickened 188 people in 24 states – was fueled by parents who decided not to vaccinate their children. The majority of measles patients were unvaccinated. In July, the USA had its first measles death in 12 years when a woman in Washington state died of complications from the virus, which can lead to pneumonia and other serious illnesses.

The measles outbreak spurred California and Vermont this year to make it harder for parents for parents to "opt out" of vaccines, which are required to attend public school.

Pediatrician Wendy Sue Swanson, speaking at a press conference about the flu in Washington, said there's no evidence that delaying vaccines is safer or more effective than the standard schedule from the Centers for Disease Control and Prevention. Children today are vaccinated against 14 diseases, beginning at birth.

Skipping or delaying vaccines leaves children vulnerable to life-threatening diseases for a longer time, said Swanson, who writes a blog called Seattle Mama Doc. Multiple studies show no increased risk to children if they follow the standard vaccine schedule.

"There is no 'alternative' immunization schedule," Remley said. "Delaying vaccines only leaves a child at risk of disease for a longer period of time; it does not make vaccinating safer."

A photographer stands behind the candidate podiums before the start of the Republican debate at the Ronald Reagan Presidential Library and Museum on Sept. 16, 2015, in Simi Valley, Calif. Tom Stathis, AP

Alison Singer, president and co-founder of the Autism Science Foundation, said candidates should not politicize issues of public health.

"Donald Trump is a part of a fringe movement that includes Jenny McCarthy and others who have dangerously perpetuated the false link between vaccines and autism," Singer said. "The facts are clear. Vaccines do not cause autism. Some people may not like the facts, but they don't get to change them, even if they are running for president of the United States.

"Politicians are wrong to speak casually about altering the vaccine schedule in an effort to score political points. The CDC vaccine schedule is carefully and scientifically developed to protect children when they are most vulnerable. Many diseases are far more deadly if contracted by an infant. All vaccines are important. It's alarming that the physicians on the stage last night don't know better."

A recent CDC report calculates that vaccinations given to children from 1994 to 2013 will prevent 732,000 premature deaths in the United States.

"Vaccines work, plain and simple," Remley said. "Vaccines are one of the safest, most effective and most important medical innovations of our time. Pediatricians partner with parents to provide what is best for their child, and what is best is for children to be fully vaccinated."

A nurse gives the rotavirus vaccine to a baby during a program to start vaccination against rotavirus.(Photo: HECTOR RETAMAL, AFP/Getty Images)

At the Washington press conference, CDC officials and others urged Americans to get a flu shot. It's especially important for pregnant women to get flu shots, because the vaccines protect both them and their babies, even several months after birth, Swanson said.

At least 145 children died of the flu last year, CDC director Thomas Frieden said. Even in the best of years, flu sickens millions of Americans and kills thousands, he said.

Only about half of Americans get vaccinated against the flu each year, according to the CDC, which recommends that everyone over age 6 months be vaccinated. Flu shots made without eggs are now available and are safe for people who have allergies to eggs. Nasal spray vaccines are also available, for those who don't like needles, William Schaffner, a professor at the Vanderbilt School of Public Health, said.

Last year's flu vaccine was less effective than usual because circulating strains of influenza began mutating after the shots were manufactured. Overall, the flu vaccine reduced the risk of flu by only 19%, according to the CDC.

And the flu season was particularly severe because the dominant strain was H3N2. Those viruses always exact a high toll on seniors. And last year, the rate of hospitalization for the elderly was the highest recorded, Frieden said.

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This year's flu shots appear to be a good match for circulating viruses, Frieden said. Manufacturers have produced 171 million doses, so there is no shortage.

Many younger and middle-aged adults skip vaccines because they think they're too healthy to get sick, said Kathleen Neuzil, director of the Center for Vaccine Development at the University of Maryland School of Medicine.

But even strong, healthy people feel "flattened" by the flu, which is far more serious than a bad cold, she said. Young people are often the ones who spread the flu to vulnerable people, such as children and the elderly, Neuzil said.

"People think they're invincible," Neuzil said. "You can still get flu, and you can certainly transmit flu to people who aren't as young and healthy as you are."